S. Baraket, CRITICAL-POINTS OF THE GINZBURG-LANDAU SY STEM ON A RIEMANNIAN SURFACE, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 319(9), 1994, pp. 949-952
We study here the Ginzburg-Landau functional on a Riemannian surface S
, endowed with an arbitrary metric E(epsilon) (u) = 1/2 integral(S) \\
del u\\(2) 1/4 epsilon(2) integral(S) (\u\(2) - 1)(2), u is an element
of H-1 (S,C), where epsilon is an element of\0, infinity\. We study t
he asymptotic behaviour of the critical points for E(epsilon) as epsil
on --> 0. We define a renormalized energy which allow to characterize
the position of the singularities at the limit.